The Molarity of a solution of sulphuric acid is 1.35 M. Calculate its molality. (The density of acid solution is 1.02 g `cm^(–3)`).

Answer

To calculate the molality of a sulfuric acid solution given its molarity and density, we can follow these steps:

### Step 1: Understand Molarity
Molarity (M) is defined as the number of moles of solute per liter of solution. Given that the molarity of the sulfuric acid solution is 1.35 M, this means there are 1.35 moles of sulfuric acid (H₂SO₄) in 1 liter of solution.

### Step 2: Calculate the Mass of the Solution
Using the density of the solution, we can calculate the mass of the solution. The density is given as 1.02 g/cm³, which is equivalent to 1.02 kg/L (since 1 g/cm³ = 1000 kg/m³).

\[ \text{Mass of solution} = \text{Density} \times \text{Volume} = 1.02 \, \text{kg/L} \times 1 \, \text{L} = 1.02 \, \text{kg} \]

### Step 3: Calculate the Mass of the Solute
Next, we need to find the mass of the solute (sulfuric acid). The molar mass of H₂SO₄ is approximately 98 g/mol.

To find the mass of the solute:
\[ \text{Mass of solute} = \text{Number of moles} \times \text{Molar mass} = 1.35 \, \text{moles} \times 98 \, \text{g/mol} = 132.3 \, \text{g} \]

Convert grams to kilograms:
\[ \text{Mass of solute in kg} = \frac{132.3 \, \text{g}}{1000} = 0.1323 \, \text{kg} \]

### Step 4: Calculate the Mass of the Solvent
Now, we can find the mass of the solvent by subtracting the mass of the solute from the mass of the solution.

\[ \text{Mass of solvent} = \text{Mass of solution} - \text{Mass of solute} = 1.02 \, \text{kg} - 0.1323 \, \text{kg} = 0.8877 \, \text{kg} \]

### Step 5: Calculate Molality
Molality (m) is defined as the number of moles of solute per kilogram of solvent.

\[ \text{Molality} = \frac{\text{Number of moles of solute}}{\text{Mass of solvent in kg}} = \frac{1.35 \, \text{moles}}{0.8877 \, \text{kg}} \approx 1.52 \, \text{mol/kg} \]

### Final Answer
The molality of the sulfuric acid solution is approximately **1.52 mol/kg**.

---